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transcript

Course

Power Quality - 2

Ljubljana, Slovenia2013/14

Prof. dr. Igor Papičigor.papic@fe.uni-lj.si

Harmonics – definitions

Content

1st day 2nd day 3rd day 4th day 5th day

Session 1

Introduction to Power Quality • what is PQ • economic value • responsibilities

Harmonics – definitions • calculations • non-linear loads • harmonic

sequences

Harmonics - design of power factor correction devices • resonance points • filter design

Flicker case study • calculation of

flicker spreading in radial network

• variation of network parameters

Interruptions • definitions • reliability indices • improving

reliability

Session 2

Basic terms and definitions • voltage quality • continuity of

supply • commercial

quality

Propagation of harmonics • sources • consequences • cancellation

Flicker - basic terms • voltage variation • flicker frequency • sources • flickermeter

Voltage sags – definitions • characteristics • types • causes

Consequences of inadequate power quality • voltage quality • interruptions • costs

Session 3

PQ standards • EN 50 160 • other standards • limit values

Harmonics - resonances in network • parallel

resonance • series resonance

Flicker spreading • radial network • mashed network • simulation • examples

Propagation of voltage sags • transformer

connections • equipment

sensitivity • mitigation

Modern compensation devices • active and hybrid

compensators • series and shunt

compensators

Session 4

PQ monitoring • measurements • PQ analyzers • data analyses

Harmonics case study • calculation of

frequency impedance characteristics

Flicker mitigation • system solutions

– network enforcement

• compensation

Other voltage variations • unbalance • voltage

transients • overvoltages

Conclusions • PQ improvement

and costs • definition of

optimal solutions

Power Quality, Ljubljana, 2013/14 3

Harmonics - definitions

– harmonics are sinusoidal voltages or currents having frequencies that are integer multiples of the frequency at which the supply system is designed to operate (fundamental frequency -50 Hz or 60 Hz)

• harmonic distortion – steady-state deviation from an ideal sine wave

• harmonic distortion is caused by nonlinear loads • current is not proportional to the applied voltage

• some load equipment does not draw a sinusoidal current from a perfectly sinusoidal voltage source

• the relationship between voltage and current at every instant of time is not constant, i.e., the load is non-linear

• harmonic currents flowing through the system impedance results in harmonic voltages at the load

• current vs. voltage distortion

Current vs. voltage distortion

• three-phase electronic load

• three-phase electronic load –increased current

• example of distorted voltage and current– supply voltage and current – Faculty of EE, Ljubljana

Fourier series

• well established methods for circuit analysis with sinusoidal voltage and current sources

• Fourier series-framework for circuit analysis with periodic non-sinusoidal voltage and current sources– decomposition into harmonic components.– each periodic function can be expressed as a sum of

pure sine waves– frequency of each sinusoid is an integer multiple of the

fundamental frequency

Fourier series

⋅⎟⎠⎞

⎜⎝⎛ ⋅⋅⋅=

⋅⎟⎠⎞

⎜⎝⎛ ⋅⋅⋅=

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ ⋅⋅⋅+⎟

⎠⎞

⎜⎝⎛ ⋅⋅⋅+⋅=

2sin)(2

2cos)(2

component dc)(2

2sin2cos21

Fourier series

( ) ∑

⎟⎠⎞

⎜⎝⎛ +⋅⋅⋅+⋅=

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ ⋅⋅⋅+⎟

⎠⎞

⎜⎝⎛ ⋅⋅⋅+⋅=

2sin21

2sin2cos21

Fourier series

• odd symmetry

• even symmetry

∫ ⋅⎟⎠⎞

⎜⎝⎛ ⋅⋅⋅=

=−−=

2sin)(4

2cos)(4

)()(2/

⋅⎟⎠⎞

⎜⎝⎛ ⋅⋅⋅=

Fourier series

• odd harmonics in the system

– positive and negative half-cycles of a waveform have identical shapes

• even harmonics in the system

– something wrong– voltage fluctuation

(flicker)

Fourier series

• convergence– square wave– 4. components

Fourier series

• convergence– triangle– 2. components

Fourier series

• decomposition of a distorted waveform into harmonic components

Decomposition into harmonic components

• triangle wave

• three-phase bridge rectifier

• notched voltage

• flat-top voltage

Total harmonic distortion – THD

• THD – measure of the effective (rms) value of harmonic distortion (this may show high relative distortion even though the magnitude of the current may be low)

• h – order of harmonic• M – rms value of h-th harmonic

Total demand distortion – TDD

• Ih – magnitude of the individual harmonic components• IL – maximum demand load current (rms amps) at the

fundamental frequency at the point of common coupling –PCC (annual average)

• fundamental harmonic of the sample may change over time

Power and distortion

• apparent power– represents required

system capacity

• active power– represents energy

consumption

rmsrms IUS ⋅=

hhIUP ϕ∑∞

∑∞

hhrms UU ∑

hhrms II

Power and distortion

• reactive power

• distortion VA– is not a conservative

quantity

hhIUQ ϕ∑∞

222 QPSD −−=

Power factor and distortion

• displacement power factor

• true power factor

SPDPF =

SPTPF h

hhh∑∞

Harmonics in balanced 3-phase system

– harmonics of order h = 3, 9, 15, 21, 27, ... are purely zero sequence

– harmonics of order h = 5, 11, 17, 23, ... are purely negative sequence

– harmonics of order h = 7, 13, 19, 25, ... are purely positive sequence

– will be harmonics of order h = 3, 9, 15, ... always compensated in delta winding of a transformer

– neutral line!

Harmonic sequences

– 3. harmonic – zero sequence

Harmonic sequences

– 3. harmonic – positive sequence

Harmonic sequences

– 3. harmonic – negative sequence

Harmonic sequences

Propagation of harmonics

Content

Session 1

sequences

reliability

Session 2

quality

Session 3

compensators

Session 4

• compensation

optimal solutions

Sources of harmonic distortion

• saturable devices – electromagnetic devices with a steel core– nonlinear magnetizing characteristics of the steel– transformers, rotating machines, non-linear reactors

• power electronics based converters– VSD, DC motor drives, electronic power supplies,

rectifiers, inverters, SVCs, HVDC transmission

• arcing devices – induction and arc furnaces, welding machines, ...– fluorescent lighting

• transformer saturation – non-sinusoidal exciting current though less then 1% of

rated full load current – odd harmonics and triplens– due to dc component of this current even harmonics are

also possible• rotating machines

– varying magnetic field reluctance– THDV typically less then 3%

• arc furnaces – non-linear V/I characteristic of the arc – 2nd, 4th harmonic

• arc welding – non-linear V/I characteristic of the arc

• fluorescent lighting – non-linear V/I characteristic of the arc

• power electronics– electronic power supply– battery chargers– Variable Speed Drives – VSD– DC motor drives– rectifier/inverter applications

• elements of power system– transformers– compensators (resonances)

• industrial loads– power electronics– arc furnaces

• households and commercial buildings– lighting– switch mode power supplies

Examples of nonlinear loads

• single-phase power supplies

• current and harmonic spectrum for switch mode power supply (SMPS)– triplen

harmonics

• fluorescent lamp current and spectrum– magnetic ballast

• fluorescent lamp current and spectrum– electronic ballast

• three-phase power converters

• current and harmonic spectrum for adjustable speed drive(ASD)

• transformer magnetizing current and harmonic spectrum

• semiconductor devices– rectifiers, inverters, frequency converters– most frequent source of voltage distortion

Type of load Typical waveform Current distortion THD

Single PhasePower Supply

80 % (high 3rd)

Semiconverter

high 2nd, 3rd, 4th at partial loads

• semiconductor devicesType of load Typical waveform Current distortion THD

6-Pulse Converter, capacitive smoothing, no series inductance

6-Pulse Converter, capacitive smoothing with series

inductance > 3%, or dc drive

AC VoltageRegulator

varies with firing angle

• semiconductor devices

Type of load Typical waveform Current distortion THD

12-Pulse Converter

AC VoltageRegulator

varies with firing angle

• representation of a nonlinear load

• harmonic sources in the network– equivalent

schemes

Consequences of harmonic distortion

– additional losses – accelerated insulation ageing

• thermal stress – through increasing copper, iron and dielectric losses

• harmonic distortion generates high current crest factor (the ratio of peak current and RMS current)

• insulation stress – through the increase of peak voltage (voltage crest factor)

• dielectric breakdown of insulated cables

– harmless for heating bodies

– motors and generators• overheating• decreased efficiency• vibrations• high-pitched noises

– interference in communication circuits

– high neutral currents (triplen harmonics)

– high neutral currents• transformer connection• neutral to earth voltages

create common mode noise problems

• circulating currents flowing in transformers

• high voltage drop at loads

• failure of neutral conductor

– resonance – reactive power compensation• capacitor or transformer failure• capacitor fuse blowing• transformer overheating at less than full load and

decreased efficiency– unstable operation of zero-crossing firing

circuits• semiconductors devices

– protection• nuisance tripping• fuses malfunction (both, due to higher harmonics and

spikes)• failure of ground fault relaying (due to excessive third

harmonic currents in the neutral 20-25% of the fundamental current)

– interference with power meters – induction disk W-meters

• the error can be as high as 35%• biggest error in measuring demand (no account of D)• measured demand is less than actual in particular

when THD>10% (customer pays less!?)– ...

Harmonic cancellation

• modification of system frequency response– system impedance - resonances– reactive power compensation– detuned filters

• passive compensation– passive elements (capacitors, inductors)– resonance

• active compensation– source of harmonic current or voltage– universal solution– price

• system measures• equipment manufacturer measures

– modification of system frequency response• real case• classical reactive power compensation

– load-side frequency characteristics– resonance at 5th in 7th harmonic

• compensation with detuned filters– load-side frequency characteristics– partial renovation of compensators

– modification of system frequency response• real case

– modification of system frequency response• classical reactive power compensation - load-side

frequency characteristics

– modification of system frequency response• compensation with detuned filters - load-side

frequency characteristics

– modification of system frequency response• resonance could be caused by current or voltage

harmonics, which are under “normal” operating conditions well below limit values (EN 50160)

• modification of system frequency response eliminates resonance

– eliminated amplification– no harmonic cancellation

– passive compensation –passive filters

• resonance problem– constant short-circuit power– close to a harmonic source

• parallel and series resonance circuit

• different configurations– single-tuned filter– double-tuned filter– ...

– active compensation• based on voltage sourced converter - VSC

– IGBTs– pulse width modulation - PWM

– active compensation• parallel connected active filter

voltagesourced

converter

– active compensation• series connected active filter

I s I LUp

voltagesourced

converter

– active compensation• Unified Power Quality Conditioner - UPQC

I s I L

series AF parallel AF

– active compensation• hybrid filter

voltage sourced

converter

passivefilter

– active compensation• general application

– active compensation

• simulation of parallel active filter operation

– active compensation• simulation of parallel hybrid filter operation

– active compensation– no influence on system impedance– on-line adaptation– series harmonic compensation possible only with active

filter– dynamic (quick response) compensation– compensation of other disturbances

» flicker» voltage dips» unbalance

– price!!

– system measures• electrical separation of disturbing loads• increased short-circuit power

– equipment manufacturer measures• compensation within devices• use of converters with efficient smoothing• use of multi-pulse converters• use of PWM with high switching frequency

– equipment manufacturer measures• example of non-compensated and compensated

compact fluorescent lamp

Harmonics – resonances in network

Content

Session 1

sequences

reliability

Session 2

quality

Session 3

compensators

Session 4

• compensation

optimal solutions

Resonances in network

• possible resonance between reactive power compensator and network impedance– series resonance– parallel resonance

• procedure of determination of potential resonance problems– resonance frequencies close to characteristic harmonics– actual presence of harmonics

• analysis of two practical cases

• frequency impedance characteristics– possible resonance – connection of capacitance

(capacitor banks) and inductance (lines, transformers,...)

• frequency impedance characteristics– resonance – inductive reactance equals capacitive

reactance

πωω

• frequency impedance characteristics– series resonance

• series connection of capacitor and inductor

∞→→

→→

ffjXUffI

ffjXCfj

LfjfjXπ

• frequency impedance characteristics– parallel resonance

• parallel connection of capacitor and inductor

∞→→

→→

ffjBIffU

CfjLfj

fjB ππ

UI L C

Resonances in network – case 1

• frequency impedance characteristics– example of supply network

• frequency impedance characteristics– example of supply network – equivalent circuit

• frequency impedance characteristics– voltage harmonic source is on the network side

• impedance from the network side• series resonance

1)(Z)(Z)(Z1

ωωω

• frequency impedance characteristics– harmonic source

is on the network side

• impedance characteristics as a function of frequency

• impedance characteristics as a function of number of used compensation stages

• frequency impedance characteristics– current harmonic source is on the load side

• impedance from the load side• parallel resonance

)(Z)(Z1

ωωωω

TRSCCL +++

is on the load side

• impedance characteristics as a function of number of used compensation stages

• frequency impedance characteristics– example of supply network – conclusions based on

performed analysis• possible series resonance at 11th harmonic if 4, 5 or 6

compensation stages are used • possible series resonance at 13th harmonic if 3, 4 or 5

compensation stages are used • possible parallel resonance at 11th harmonic if 5

compensation stages are used • possible parallel resonance at 13th harmonic if 3

compensation stages are used

– frequency impedance characteristics• real case 2

– frequency impedance characteristics• classical reactive power compensation• network-side equivalent circuit

– frequency impedance characteristics• classical reactive power compensation• network-side frequency characteristics

– frequency impedance characteristics• classical reactive power compensation• load-side equivalent circuit

– frequency impedance characteristics• classical reactive power compensation• load-side frequency characteristics

– frequency impedance characteristics• problem

– resonance at 5th and 7th harmonic– renovation of first 4 stages (K1, K2, K3 and K4)

• solution– renovated stages as detuned filters– solution for operation with 2 old stages – classical

compensators (K5 in K6)

– frequency impedance characteristics• compensation with detuned filters• network-side frequency characteristics

– frequency impedance characteristics• compensation with detuned filters• load-side frequency characteristics

– frequency impedance characteristics• measurements results

• determination of harmonic sources– harmonic current vector method– network and load side

– frequency impedance characteristics• simulation results

– classical reactive power compensation– 5th harmonic

– frequency impedance characteristics• simulation results

– compensation with detuned filters– 5th harmonic

Harmonics case study

Content

Session 1

sequences

reliability

Session 2

quality

Session 3

compensators

Session 4

• compensation

optimal solutions

Case study – frequency response

• frequency impedance characteristics– example of supply network

• frequency impedance characteristics– example of supply network – data for calculation

• network equivalent– short-circuit power

– rated voltage

– ratio R/X

MVA 80=scS

kV 20=MVU

10/1)/( =SCXR

• 2 x transformer 20/0,4 kV– short-circuit voltage

– rated power

– rated voltage

– ratio R/X

% 13,4=scu

kV 4,0kV; 20 == LVMV UU

4/1)/( =TRXR

MVA 63,0 x 2=nS

• load– rated voltage

– active power

– reactive power

kV 4,0=LVU

MW 54,0=LP

MVAr 46,0=LQ

• compensator– rated voltage

– reactive power

– ratio R/X

MVAr 40,0=CQ

kV 4,0=LVU

50/1)/( =CXR

• frequency impedance characteristics– example of supply network – equivalent circuit

• frequency impedance characteristics– example of supply network – calculation of parameters in

equivalent circuit (the same voltage level ULV)• network equivalent

SCSCSC

LfjRfjZXR

m 199,0)/(1

μH 33,6)/(1

equivalent circuit (the same voltage level ULV)• transformer

TRTRTR

LfjRfjZXR

XRuSUR

m 27,1)/(1

)/(100

μH 2,16)/(1

1100100

equivalent circuit (the same voltage level ULV)• load

LfjRfjZQP

mH 466,0502

equivalent circuit (the same voltage level ULV)• compensator

CfjRfjZ

πππ

221)2(

m 8)/(1

mF 96,7)/(1100

−=+=

• frequency impedance characteristics– harmonic source is on the network side

• impedance from the network side• series resonance

)2(Z)(Z valueabsolute

1)(Z)(Z)(Z

ωωω

• frequency impedance characteristics– harmonic source is on the load side

• impedance from the load side• parallel resonance

)2(Z)(Z valueabsolute

)(Z)(Z1

TRSCCL

ωωωω

is on the load side

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